Representation type of Jordan algebras

Author(s)

Kashuba, Iryna ^[1] ; Ovsienko, Serge ^[2] ; Shestakov, Ivan ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05311970 Sao Paulo - Brazil

^[2] Kiev Tarns Shevchenko Univ, Fac Mech & Math, UA-00133 Kiev - Ukraine

• Document type: Journal article
• Source: ADVANCES IN MATHEMATICS; v. 226, n. 1, p. 385-418, JAN 15 2011.
• Web of Science Citations: 5

Abstract

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 04/02850-2 - Sergiy Ovsiyenko | University Kiev - Ukraine
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 05/60337-2 - Lie and Jordan algebras, their representations and generalizations
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants